KMnO_4 acts as an oxidising agent in acidic medium. ' X ' is the...

\underset{(\mathrm{O}. \mathrm{A})}{\stackrel{+7}{\mathrm{KMnO}}} \xrightarrow{\text{ Acidic medium }} \mathrm{Mn}^{2+}$<br />X is difference in oxidation state.<br />$6 \mathrm{CH}_3 \mathrm{COO}^{\ominus}+\mathrm{Fe}^{3+}+\mathrm{H}_2 \mathrm{O} \rightarrow\left[\mathrm{Fe}_3\left(\mathrm{OH}_2\right)\left(\mathrm{CH}_3 \mathrm{COO}\right)_6\right]^{\oplus}+2 \mathrm{H}^{\oplus}$<br />\left[\mathrm{Fe}_3(\mathrm{OH})_2\left(\mathrm{CH}_3 \mathrm{COO}\right)_6\right]^{\oplus} \text{(Brown red ppt)} +4 \mathrm{H}_2 \mathrm{O}\rightarrow\left[\mathrm{Fe}(\mathrm{OH})_2\left(\mathrm{CH}_3 \mathrm{COO}\right]+\mathrm{CH}_3 \mathrm{COOH}+\mathrm{H}^{\oplus}\right.<br />\mathrm{Fe}^{3+}$\Rightarrow 3 $\mathrm{~d}^5 4 \mathrm{~s}^0$contains 5 d electrons
So $Y=5$
$X+Y=5+5=10$